Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C337 ⋊ C4 |
| Sylow | C337 ⋊ #117 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=e,c^2=d,b^a=bd,f^a=f^148,f^e=f^336692 conjugacy classes — view the full character table.
| maximal subgroup of | #36342172, #36342173, #36342176, … |
| maximal normal subgroup of | #36342172, #36342173, #36342176, … |
| maximal quotient of | #36342241, C4×C22⋊#13062438, C4×C4⋊#13062438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 225);